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Algebra i logika, 2022, Volume 61, Number 2, Pages 127–149
DOI: https://doi.org/10.33048/alglog.2022.61.201 (Mi al2702) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Method of verbal operations and automorphisms of the category of free algebras

E. V. Aladova

Universidade Federal do Rio Grande do Norte, Lagoa Nova
Full-text PDF (1061 kB) Citations (3)
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DOI: https://doi.org/10.33048/alglog.2022.61.201
Abstract: Let an arbitrary variety of algebras and the category of all free finitely generated algebras in that variety be given. This paper is the second in a series of papers started in [Algebra and Logic, 61, No. 1, 1—15 (2022)] where we deal with automorphisms of the category of free finitely generated algebras. Here we describe in detail a method of verbal operations. The method provides a characterization of automorphisms of the category of all free finitely generated algebras in a given variety. The characterization plays a crucial role in universal algebraic geometry. We supply the reader with illuminating examples which clarify the method.
Keywords: variety of algebras, category of free finitely generated algebras, universal algebraic geometry over arbitrary variety of algebras, group of automorphisms, method of verbal operations.
Funding agency Grant number
Israel Science Foundation 1623/16
1994/20
Bar-Ilan University
E. V. Aladova is supported by the ISF grants 1623/16, 1994/20, and by Gelbart Institute for Mathematical Sciences, Department of Mathematics, Bar-Ilan University, Israel
Received: 28.04.2021
Revised: 01.09.2022
English version:
Algebra and Logic, 2022, Volume 61, Issue 2, Pages 87–103
DOI: https://doi.org/10.1007/s10469-022-09679-7
Bibliographic databases:
Document Type: Article
UDC: 512.54.05+512.57
Language: Russian
Citation: E. V. Aladova, “Method of verbal operations and automorphisms of the category of free algebras”, Algebra Logika, 61:2 (2022), 127–149; Algebra and Logic, 61:2 (2022), 87–103
Citation in format AMSBIB
\Bibitem{Ala22}
\by E.~V.~Aladova
\paper Method of verbal operations and automorphisms of the category of free algebras
\jour Algebra Logika
\yr 2022
\vol 61
\issue 2
\pages 127--149
\mathnet{http://mi.mathnet.ru/al2702}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4510193}
\transl
\jour Algebra and Logic
\yr 2022
\vol 61
\issue 2
\pages 87--103
\crossref{https://doi.org/10.1007/s10469-022-09679-7}
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  • https://www.mathnet.ru/eng/al/v61/i2/p127
    Cycle of papers
    This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
     
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